V. N. Popov, “The number of integer points under a parabola”, Mat. Zametki, 18:5 (1975), 699–704; Math. Notes, 18:5 (1975), 1007

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Matematicheskie Zametki, 1975, Volume 18, Issue 5, Pages 699–704 (Mi mzm7681)

This article is cited in 5 scientific papers (total in 5 papers)

The number of integer points under a parabola

V. N. Popov

Leningrad Department of V. A. Steklov Institute of Mathematics, Academy of Sciences of the USSR

Full-text PDF (371 kB) Citations (5)

Abstract: The remainder term for the number of integer points under the parabola in the region

$0<x\le b\le a$ ,

$0<y\le x^2/a$ admits a bound

$O(a^{1/2+c\ln\ln a})$ with the unimprovable exponent 1/2.

Received: 01.04.1975

English version:
Mathematical Notes, 1975, Volume 18, Issue 5, Pages 1007–1010
DOI: https://doi.org/10.1007/BF01153567

Bibliographic databases:

UDC: 511

Language: Russian

Citation: V. N. Popov, “The number of integer points under a parabola”, Mat. Zametki, 18:5 (1975), 699–704; Math. Notes, 18:5 (1975), 1007–1010

Citation in format AMSBIB

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\paper The number of integer points under a~parabola

\jour Mat. Zametki

\yr 1975

\vol 18

\issue 5

\pages 699--704

\mathnet{http://mi.mathnet.ru/mzm7681}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=396451}

\zmath{https://zbmath.org/?q=an:0317.10056}

\transl

\jour Math. Notes

\yr 1975

\vol 18

\issue 5

\pages 1007--1010

\crossref{https://doi.org/10.1007/BF01153567}

Linking options:

https://www.mathnet.ru/eng/mzm7681

https://www.mathnet.ru/eng/mzm/v18/i5/p699

This publication is cited in the following 5 articles:

O. M. Fomenko, “On the distribution of fractional parts of polynomials of two variables”, J. Math. Sci. (N. Y.), 193:1 (2013), 129–135
O. M. Fomenko, “On the distribution of fractional parts of polynomials”, J. Math. Sci. (N. Y.), 184:6 (2012), 770–775
Günter Horn, “Gitterpunkte über einem hyperbolischen Paraboloid”, Mathematische Nachrichten, 162:1 (1993), 153
Werner Georg Nowak, Lecture Notes in Mathematics, 1114, Zahlentheoretische Analysis, 1985, 98
Werner Georg Nowak, “Gitterpunkte in Lemniskatenscheiben”, Manuscripta Math, 39:2-3 (1982), 277

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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